Weak Gravitational Lensing in Fourth Order Gravity

For a general class of analytic $f(R,R_{\alpha\beta}R^{\alpha\beta},R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta})$ we discuss the gravitational lensing in the Newtonian Limit of theory. From the properties of Gauss Bonnet invariant it is successful to consider only two curvature invariants between the Ricci and Riemann tensor. Then we analyze the dynamics of photon embedded in a gravitational field of a generic $f(R,R_{\alpha\beta}R^{\alpha\beta})$-Gravity. The metric is time independent and spherically symmetric. The metric potentials are Schwarzschild-like, but there are two additional Yukawa terms linked to derivatives of $f$ with respect to two curvature invariants. Considering the case of a point-like lens, and after of a generic matter distribution of lens, we study the deflection angle and the images angular position. Though the additional Yukawa terms in the gravitational potential modifies dynamics with respect to General Relativity, the geodesic trajectory of photon is unaffected by the modification in the action by only $f(R)$. While we find different results (deflection angle smaller than one of General Relativity) only thank to introduction of a generic function of Ricci tensor square. Finally we can affirm the lensing phenomena for all $f(R)$-Gravities are equal to the ones known from General Relativity. We conclude the paper showing and comparing the deflection angle and image positions for $f(R,R_{\alpha\beta}R^{\alpha\beta})$-Gravity with respect to ones of General Relativity.Comment: 11 pages, 5 figure

Conformal Transformations and Weak Field Limit of Scalar-Tensor Gravity

The weak field limit of scalar tensor theories of gravity is discussed in view of conformal transformations. Specifically, we consider how physical quantities, like gravitational potentials derived in the Newtonian approximation for the same scalar-tensor theory, behave in the Jordan and in the Einstein frame. The approach allows to discriminate features that are invariant under conformal transformations and gives contributions in the debate of selecting the true physical frame. As a particular example, the case of $f(R)$ gravity is considered.Comment: 11 pages, preliminary versio

Galaxy rotation curves in f(R,ϕ)f(R,\phi)-gravity

We investigate the possibility to explain theoretically the galaxy rotation curves by a gravitational potential in total absence of dark matter. To this aim an analytic fourth-order theory of gravity, nonminimally coupled with a massive scalar field is considered. Specifically, the interaction term is given by an analytic function $f(R,\phi)$ where $R$ is the Ricci scalar and $\phi$ is the scalar field. The gravitational potential is generated by a point-like source and compared with the so called Sanders's potential that can be exactly reproduced in this case. This result means that the problem of dark matter in spiral galaxies could be fully addressed by revising general relativity at galactic scales and requiring further gravitational degrees of freedom instead of new material components that have not been found out up to now.Comment: 17 pages, 6 figures. To appear in Phys. Rev.

Fourth order gravity and experimental constraints on Eddington parameters

PPN-limit of higher order theories of gravity represents a still controversial matter of debate and no definitive answer has been provided, up to now, about this issue. By exploiting the analogy between scalar-tensor and fourth-order theories of gravity, one can generalize the PPN-limit formulation. By using the definition of the PPN-parameters $\gamma$ and $\beta$ in term of the $f(R)$ derivatives, we show that a family of third-order polynomial theories, in the Ricci scalar $R$, turns out to be compatible with the PPN-limit and the deviation from General Relativity theoretically predicted agree with experimental data.Comment: 7 pages, 3 figure

The Quadratic Coefficient of the Electron Cloud Mapping

The Electron Cloud is an undesirable physical phenomenon which might produce single and multi-bunch instability, tune shift, increase of pressure ultimately limiting the performance of particle accelerators. We report our results on the analytical study of the electron dynamics.Comment: 5 pages, 7 figures, presented at ECLOUD12: Joint INFN-CERN-EuCARD-AccNet Workshop on Electron-Cloud Effects, La Biodola, Isola d Elba, Italy, 5-9 June 201